Noise Reduction in Coherence Scanning Interferometry for Surface Topography Measurement

Evaluation of High-Frequency Measurement Errors from Turned Surface Topography Data Using Machine Learning Methods

Manufacturing processes in industry applications are often controlled by the evaluation of surface topography. Topography, in its overall performance, includes form, waviness, and roughness. Methods of measurement of surface roughness can be roughly divided into tactile and contactless techniques. The latter ones are much faster but sensitive to external disturbances from the environment. One type of external source error, while the measurement of surface topography occurs, is a high-frequency noise. This noise originates from the vibration of the measuring system. In this study, the methods for reducing high-frequency errors from the results of contactless roughness measurements of turned surfaces were supported by machine learning methods. This research delves into optimizing filtration methods for surface topography measurements through the application of machine learning models, focusing on enhancing the accuracy of surface roughness assessments. By examining turned surfaces under specific machining conditions and employing a variety of digital filters, the study identifies the Gaussian regression filter and spline filter as the most effective methods at a 22.5 µm cut-off. Utilizing neural networks, support vector machines, and decision trees, the research demonstrates the superior performance of SVMs, achieving remarkable accuracy and sensitivity in predicting optimal filtration methods.

Simulation-driven machine learning approach for high-speed correction of slope-dependent error in coherence scanning interferometry

Slope-dependent error often occurs in the coherence scanning interferometry (CSI) measurement of functional engineering surfaces with complex geometries. Previous studies have shown that these errors can be corrected through the characterization and phase inversion of the instrument's three-dimensional (3D) surface transfer function. However, since CSI instrument is usually not completely shift-invariant, the 3D surface transfer function characterization and correction must be repeated for different regions of the full field of view, resulting in a long computational process and a reduction of measurement efficiency. In this work, we introduce a machine learning approach based on a deep neural network that is trainable for slope-dependent error correction in CSI. Our method leverages a deep neural network to directly learn errors characteristics from simulated surface measurements provided by a previously validated physics-based virtual CSI method. The experimental results demonstrate that the trained network is capable of correcting the surface height map with 1024 × 1024 sampling points within 0.1 seconds, covering a 178 µm field of view. The accuracy is comparable to the previous phase inversion approach while the new method is two orders of magnitude faster under the same computational condition.

Height Fluctuations and Surface Gradients in Topographic Measurements

Topographic maps are composed of pixels associated with coordinates (x, y, z) on a surface. Each pixel location (x, y) is linked with fluctuations in a measured height sample (z). Fluctuations here are uncertainties in heights estimated from multiple topographic measurements at the same position. Height samples (z) are measured at individual locations (x, y) in topographic measurements and compared with gradients on topographies. Here, gradients are slopes on a surface calculated at the scale of the sampling interval from inclination angles of vectors that are normal to triangular facets formed by adjacent height samples (z = z(x, y)). Similarities between maps of gradients logs and height fluctuations are apparent. This shows that the fluctuations are exponentially dependent on local surface gradients. The highest fluctuations correspond to tool/material interactions for turned surfaces and to regions of maximum plastic deformation for sandblasted surfaces. Finally, for abraded, heterogeneous, multilayer surfaces, fluctuations are dependent on both abrasion and light/sub-layer interactions. It appears that the natures of irregular surface topographies govern fluctuation regimes, and that regions which are indicative of surface functionality, or integrity, can have the highest fluctuations.

Quality inspection of cube beam splitters by a white light interferometric approach

Beam splitters have a wide range of applications as a key component in optical systems. Adopting beam splitters with geometric defects in an optical system, e.g., an interferometric measurement system, may cause additional optical path difference and degrade the measurement accuracy. The quality inspection of beam splitters is essential to meet the accuracy requirements for modern optical systems. Most of the current quality inspection methods rely on inefficient and inaccurate manual observation. Therefore, for commonly used cube beam splitters (CBSs), we propose a digital method to quantify the geometric quality based on the white light interferometric principle. A Fourier domain analysis is used to calculate the CBS misalignment error and perpendicularity error. This method is verified by inspecting six different CBS samples. The experimental results show that all samples have varying degrees of misalignment and perpendicularity errors. The maximum perpendicularity error is 0.93°, and three of the six samples have misalignment errors larger than 50 µm. Nanometer level precision of the misalignment measurement can be achieved.

Top-down Determination of Fluctuations in Topographic Measurements

A top-down method is presented and studied for quantifying topographic map height (z) fluctuations directly from measurements on surfaces of interest. Contrary to bottom-up methods used in dimensional metrology, this method does not require knowledge of transfer functions and fluctuations of an instrument. Fluctuations are considered here to be indicative of some kinds of uncertainties. Multiple (n), successive topographic measurements (z = z(x,y)) are made at one location without moving the measurand relative to the measurement instrument. The measured heights (z) at each position (x,y) are analyzed statistically. Fluctuation maps are generated from the calculated variances. Three surfaces were measured with two interferometric measuring microscopes (Bruker ContourGT™ and Zygo NewView™ 7300). These surfaces included an anisotropic, turned surface; an isotropic, sandblasted surface; and an abraded, heterogeneous, multilayer surface having different, complex, multiscale morphologies. In demonstrating the method, it was found that few non-measured points persisted for all 100 measurements at any location. The distributions of uncertainties are similar to those of certain features on topographic maps at the same locations, suggesting that topographic features can augment measurement fluctuations. This was especially observed on the abraded ophthalmic lens; a scratch divides the topographic map into two zones with different uncertainty values. The distributions of fluctuations can be non-Gaussian. Additionally, they can vary between regions within some measurements.

Thresholding Methods for Reduction in Data Processing Errors in the Laser-Textured Surface Topography Measurements

There are many factors influencing the accuracy of surface topography measurement results: one of them is the vibrations caused by the high-frequency noise occurrence. It is extremely difficult to extract results defined as noise from the real measured data, especially the application of various methods requiring skilled users and, additionally, the improper use of software may cause errors in the data processing. Accordingly, various thresholding methods for the minimization of errors in the raw surface topography data processing were proposed and compared with commonly used (available in the commercial software) techniques. Applied procedures were used for the minimization of errors in the surface topography parameters (from ISO 25178 standard) calculation after the removal and reduction, respectively, of the high-frequency noise (S-filter). Methods were applied for analysis of the laser-textured surfaces with a comparison of many regular methods, proposed previously in the commercial measuring equipment. It was found that the application of commonly used algorithms can be suitable for the processing of the measured data when selected procedures are provided. Moreover, errors in both the measurement process and the data processing can be reduced when thresholding methods support regular algorithms and procedures. From applied, commonly used methods (regular Gaussian regression filter, robust Gaussian regression filter, spline filter and fast Fourier transform filter), the most encouraging results were obtained for high-frequency noise reduction in laser-textured details when the fast Fourier transform filter was supported by a thresholding approach.

Quality Assessment of a Novel Camera-Based Measurement System for Roughness Determination of Concrete Surfaces-Accuracy Evaluation and Validation

The roughness of a surface is a decisive parameter of a material. In rehabilitation of concrete structures, for example, it significantly affects the adhesion between the coating material and the base concrete. However, the standard measurement procedure in construction suffers from considerable disadvantages, which leads to the demand for more sophisticated methods. In a research project, we, therefore, developed a novel camera-based measurement system, which is customized to meet the prevailing requirements for practical use on construction sites. In this article, we provide an overview of the measurement system and present comprehensive examinations to evaluate the accuracy and to provide evidence of validity. First, we examined the accuracy of the system by empirically assessing both trueness and precision of measurements using three concrete specimens. Trueness was determined by comparing the surface measurements to those of a highly accurate microscope system, revealing RMSE values of around 40–50 µm. Precision, on the other hand, was assessed considering the scattering of the roughness measurements under repeat conditions, which led to standard deviations of less than 6 µm. Furthermore, to proof validity, a comparative study was conducted based on sixteen concrete specimens, which includes the sand patch method and laser triangulation as established roughness measurement methods in practice. The empirically determined correlation coefficients between all three methods were greater than 0.99, indicating extraordinarily high linear relationships. Among them, the greatest correlation was between the camera-based system and laser triangulation.

Chromatic confocal sensor-based sub-aperture scanning and stitching for the measurement of microstructured optical surfaces

The noncontact optical probe-based surface scanning is promising for the measurement of complex-shaped optical surfaces. In this study, by combining a chromatic confocal sensor and a planar nano-positioning stage, a sub-aperture scanning and stitching method is developed for the noncontact measurement of the microstructured optical surfaces, with the measured form accuracy being irrespective of the accuracy of the global scanning stage. After the scanning, the Gaussian process-based denoising is employed to remove the measurement noises, and a hybrid registration algorithm is proposed to achieve a 6-DOF alignment of any neighbored sub-apertures. For the registration, the differential evolution-based minimization is implemented to find a coarse transformation which then serves as the initial value for the iterative closest point-based fine registration. The hybrid method is beneficial in finding an optimal registration with a greatly reduced computation burden. Finally, the effectiveness of the developed measurement system, as well as the stitching algorithm, is comprehensively demonstrated through practically measuring a sinusoidal micro-grid surface.

Suppression of the High-Frequency Errors in Surface Topography Measurements Based on Comparison of Various Spline Filtering Methods

The metrology of so-called “engineering surfaces” is burdened with a substantial risk of both measurement and data analysis errors. One of the most encouraging issues is the definition of frequency-defined measurement errors. This paper proposes a new method for the suppression and reduction of high-frequency measurement errors from the surface topography data. This technique is based on comparisons of alternative types of noise detection procedures with the examination of profile (2D) or surface (3D) details for both measured and modelled surface topography data. In this paper, the results of applying various spline filters used for suppressions of measurement noise were compared with regard to several kinds of surface textures. For the purpose of the article, the influence of proposed approaches on the values of surface topography parameters (from ISO 25178 for areal and ISO 4287 for profile standards) was also performed. The effect of the distribution of some features of surface texture on the results of suppressions of high-frequency measurement noise was also closely studied. Therefore, the surface topography analysis with Power Spectral Density, Autocorrelation Function, and novel approaches based on the spline modifications or studies of the shape of an Autocorrelation Function was presented.

Event based coherence scanning interferometry

Coherence scanning interferometry enables high precision measurements in manifold research and industry applications. In most modern systems, a digital camera (CCD/CMOS) is used to record the interference signals for each pixel. When measuring steep surfaces or using light sources with a broad wavelength spectrum, only a small area of the sensor captures useable interference signals in one frame, so a large fraction of pixels is unused. To overcome this problem and enable measurements with high dynamic range and high scan speeds, we propose the use of an event based image sensor. In these sensors, each pixel independently registers only changes in the signal, which leads to a continuous asynchronous pixel stream of information not based on fixed frame capturing. In this Letter, we show the signal generation, an implementation in a coherence scanning microscope in combination with the nanopositioning and nanometrology machine NPMM-200, and first measurements as promising results for event based interferometry.

Performance Analysis of Surface Reconstruction Algorithms in Vertical Scanning Interferometry Based on Coherence Envelope Detection

Optical interferometry plays an important role in the topographical surface measurement and characterization in precision/ultra-precision manufacturing. An appropriate surface reconstruction algorithm is essential in obtaining accurate topography information from the digitized interferograms. However, the performance of a surface reconstruction algorithm in interferometric measurements is influenced by environmental disturbances and system noise. This paper presents a comparative analysis of three algorithms commonly used for coherence envelope detection in vertical scanning interferometry, including the centroid method, fast Fourier transform (FFT), and Hilbert transform (HT). Numerical analysis and experimental studies were carried out to evaluate the performance of different envelope detection algorithms in terms of measurement accuracy, speed, and noise resistance. Step height standards were measured using a developed interferometer and the step profiles were reconstructed by different algorithms. The results show that the centroid method has a higher measurement speed than the FFT and HT methods, but it can only provide acceptable measurement accuracy at a low noise level. The FFT and HT methods outperform the centroid method in terms of noise immunity and measurement accuracy. Even if the FFT and HT methods provide similar measurement accuracy, the HT method has a superior measurement speed compared to the FFT method.

Fourier optics modeling of interference microscopes

We propose a practical theoretical model of an interference microscope that includes the imaging properties of optical systems with partially coherent illumination. We show that the effects on measured topography of a spatially extended, monochromatic light source at low numerical apertures can be approximated in a simplified model that assumes spatially coherent light and a linear, locally shift-invariant transfer function that accounts for optical aberrations and the attenuation of diffracted plane wave amplitudes with increasing spatial frequencies. Simulation of instrument response using this model agrees with methods using numerical pupil-plane integration and with an experimental measurement of surface topography.

State-of-the-art active optical techniques for three-dimensional surface metrology: a review [Invited]

This paper reviews recent developments of non-contact three-dimensional (3D) surface metrology using an active structured optical probe. We focus primarily on those active non-contact 3D surface measurement techniques that could be applicable to the manufacturing industry. We discuss principles of each technology, and its advantageous characteristics as well as limitations. Towards the end, we discuss our perspectives on the current technological challenges in designing and implementing these methods in practical applications.